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UNDERSTANDING PHYSICAL wziafliMi THIRD EDITION m Sffio"" >*12.3D Adamson Arth W. iur 1 Understanding Physical Chemistry Third Edition Arthur W. Adamson University of Southern California The Benjamin/Cummings Publishing Company, Inc. Men/o Park, California • Reading, Massachusetts London • Amsterdam • Don Mills, Ontario • Sydney © Copyright 1980 by The Benjamin Cummings Publishing Company, / Inc. Philippines copyright 1980 by The Benjamin/Cummings Publishing Company, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States ofAmerica. Published simultaneously in Canada. ISBN 0-8053-0128-3 BCDEFGHIJKL-MA-8543210 The Benjamin/Cummings Publishing Company, Inc. 2727 Sand Hill Road Menlo Park, CA 94025 To the students—past, present, andfuture. May their ship never sink. Preface GENERAL INTRODUCTION This collection of examination questions and worked-out answers is offered as something different from and, I hope, more helpful than the usual study aid or problems supplement for an introductory physical chemistry course. Students who follow the recommended procedure shouldfindthatthisbookcanfunctionsomethinglikea"teachingmachine" by leading them in a positive way toward a betterunderstanding ofphysical chemistry. As a very practical point, it should improve their ability to perform well on examinations. Understanding PhysicalChemistrycan be used in conjunctionwithany standard physical chemistry text, and a table at the end of the preface shows the chapterorchapters ofthisbookthatcorrelate withthechapters of several standard textbooks. Thus, even without specific assignments, students can easily use the book as a study aid. In addition, it can serve as a review for students since it is a very concise text as well as a problems book. Each chapter of Understanding Physical Chemistry begins with a brief discussion of the relevant concepts and presents required equations along with informal comments about their use. Each chapter also include a discussion ofe.g.s. and SI (Systeme Internationald'Unites) quantities. In this third edition, nearly 40 percent of the problems are new or modified and, ofthe problems where units play a role, about 20 percent are now SI. The problems have been regrouped within each chapter to allow more flexible use as a study aid, and there has been some chapter rearrangement as well as additions to the introductory portions of the chapters to enhance their usefulness and clarity. In explaining the philosophy of this book, I would like to comment briefly on the role of problems and problem solving in the teaching of physical chemistry. It is an American tradition, and basically a correct one, I believe, that the best test ofa person's understanding ofa scientific subject is his or her ability to useit. Inphysical chemistry, then, examinations in this country typically tend to stress numerical problems rather than the more philosophical essay questions. There is another aspect to the use ofnumerical problems that is important. Such problems can be just as easy orjust as hard,just as straight- General Introduction v forward orjust as subtle, as essay questions. The virtue ofthe numerical problem is therefore not in any intrinsic difference in the level of understanding required to answer it as compared to the essay question. Its value is simply that, being numerical, it is concrete, and the students are thus required to sharpen their thinking to be able to decide exactly what the question means and exactly how they will answer it. The numerical problem is thus a pedagogical device to ensure clear and unambiguous answers and to expose sloppy thinking. The type of examination problem needed to achieve this purpose is somewhat special. It cannot involvejust substitution into a set equation, or nothing much is demonstrated. It cannot involve lengthy calculation for there is not enough time. What has evolved in the physical chemistry course at the University of Southern California is a type ofproblem that requires the use of only those definitions, derivations, and equations so central that the students can reasonably be expected to know them if they have studied at all. In the examination, however, a situation that calls for a change or adaptation ofthe equation or definition is described. The change is simple and straightforward, but it nonetheless must be determined by students from an analysis of the problem. Consider the ideal gas law; a simpler equation is difficult to imagine. Yet, until they refresh their thinking, even graduate students havetrouble working the problems in Chapter 1 within the time limits. (Dare I admit that this may also be true ofsome professors?) It is not thatthe problems are intrinsically difficult. When you see the answers, they seem ridicu- lously easy and often need barely the touch ofa pocket calculator. It is just that one has to think rather carefully to seejusthowthegas law must be manipulated to fit the particular situation. Such problems are not trick problems. Each was designed to test whether students had grasped a particular aspect of a principle so well that they could recognize quickly its implicit presence in the question. Thus, the ideal gas law may seem very elementary indeed until students are asked to apply it to a situation involving a gas distributed between two interconnected flasks that are not at the same temperature. The freezing-point depression effect, whereby dissolved solute B in solvent A lowers the freezing point ofthe latter, is given by a plain enough equation whose use is easy. It is another matter to recognize that the same A equation treats the solubility of solid in solvent B, that is, to see that this is merely a restatementofafreezing-pointdepressionfromadifferent pointofviewandwithan interchange ofthelabels "solvent" and "solute." In each chapter, then, a group of centrally important equations and concepts is presented, by means of problems, in a diversity of guises. The problems are worked out in detail so that the solutions are as much a part ofthis study aid as the problems themselves. Through working the problems and studying the answers, students should gain a better per- spective and a better understanding of physical chemistry. They should develop both some ability to see that principles are relevant toasituation and the confidence to fashion or to modify equations as appropriate. vi Preface TO THE STUDENT: A SUGGESTED PROCEDURE A few points ofinformation are in order. The problems come from actual quizzes or final examinations; a real group ofphysical chemistry students has labored over each one of them! Also, the time given for working them is the time that was actually allowed. You can construct a typical quiz by selecting from a given chapter two orthree problems whose time allowance totals thirty minutes. Beginning with Chapter 4, you will find problems that require the use of partial derivatives and partial differential relationships. It will help, if you are shaky on this subject, to proceed to Appendix 1. It gives a short outline of the principal relations along with a special collection of problems that you should find helpful. Some units and conversion factors are collected in Appendix 2. The tables describing SI units and interconversion between c.g.s. and SI may be especially helpful. Also, each chapter has a section on units (just before the problems). The sections in Chapters 1, 2, 3, 8, 13, 17, and 20 will be of particular help. The concepts involved and the equations needed are given at the beginning ofeach chapteralong with some informal comments abouttheir use. Read these introductory sections carefully before starting on the problems. The problems can be treated as either open book or closed book. In mostinstances, itdoes notreally matter. Infact,itis oftenharder with open book because you waste too much time looking up equations that you should know anyway. As you start working a chapter, you may want to use the list of equations as a kind of crib sheet, but, honestly, if you need this, you are not going to be able to do the problems within the time limits. Most of the time allowance is for thinking; the actual calculations are usually quite short. Try to train yourselfnot torushintoarithmeticbefore you know where you want to go. In grading these quizzes, we allowed 80 percent credit for setting up the solution correctly and 20 percent for correct arithmetic, another reason for saving your calculator work for the last. Keep in mind, too, that the numerical data are often carefully chosen to facilitate the calculation through cancellations or through shortcuts or quick approximations. Approximations, however, should not lead to more than about 1 percent error. Numbers given to only one significant figure are to be understood as being accurate to 1 percent. If you have trouble at first as you try to solve these problems, give yourself about three times the indicated time. Then study the answer carefully. Try to see what you missed or where you went wrong in your analysis. Try to generalize your conclusion so you have something to keep in mind when going on to the nextproblem.Yourgoal is tocomplete the problem within the time limit and to have it substantially correct. Note that problems ofa given type have been collected together. To the Instructor: Some FurtherComments vii After completing a chapter, review all the problems in it. Make an outline of the various ways in which the subjects were approached. The idea is to develop a close association in your mindbetweeneachrelation- ship or principle and the ways in which it can be used. If you become discouraged, it may help your morale if you ask a graduate student to work one ofthe problems within the time limit! Best wishes and good luck! TO THE INSTRUCTOR: SOME FURTHER COMMENTS Althoughthis collectionofproblems is presentedprimarilyas adistinctive kind of study aid for students, I believe it also constitutes a good source of examination questions. The problems are almost all original. The collection is large enough (700 problems) that there is not much chance that a student having the book will remember a particular solution. If you want to make small changes in the numerical data, it might be wise to check the solution since in some cases the particular numbers used were carefully chosen to facilitate calculation. The sequence of topics is approximately that followed in the lecture course at the University of Southern California. To some extent, then, the problems become more sophisticated as one proceeds through the collection. The correlation table that follows may be useful if you are using one of the textbooks listed. A little immodesty is perhaps excusable. Understanding Physical Chemistry is a rather special book, and it is one that seems to havefound a niche. It has some international use. There is a French, a Spanish, and a Polish translation, and also (I am told) a Taiwanese edition. As a bit of nostalgia, I still hear occasionally from the "class ofthe sinking ship" to which the first edition was dedicated. Arthur W. Adamson December 1979 Los Angeles CORRELATION TABLE FOR UNDERSTANDINGPHYSICAL CHEMISTRY (UPC) Chapter in UPC corresponaHng to chapter in indicated textbook* Chapter in indicated 1 text Adamson Atkins Barrow 1 1 1 1 A 2 2 4, 5, 2 A 3 3 4, 5, 17 4 4, 5, A 6 5 5 6 7, A 4, A 6 7 7, A 6 7 11 8 7 A 8 8 9, 7 9 9, 20 11 7 10 10, 20 12 17, 18 11 12 15 17, 18 12 13, 14 15 17 13 15 17 19 14 16 17 3 15 16 17 16 16 17 18 8 17 18 17 19 18 17 3, 17 9, 12 19 17 17 9 20 19 5, 7 10 21 20 5, 7 13 22 21 19 13, 14 23 3 15 24 2 16, 20 25 13, 20 20 26 16, 21 27 16 28 16 29 15 30 31 32 33 Adamson: A.W. Adamson,A TextbookofPhysicalChemistry, 2nded., Academic Press, NewYork, 1979. Atkins: P.W. Atkins, Physical Chemistry, W. H. Freeman, San Francisco, 1978. Barrow: G. M. Barrow, Physical Chemistry, 2nd ed., McGraw-Hill, New York, 1966. flA: Appendix in UPC. viii